To find the intervals on which a function is increasing or decreasing, analyze the sign of the derivative. The function is increasing on (-infinity, -1) and (2, infinity), and decreasing on (-1, 2).
Explanation:To find the intervals on which a function is increasing or decreasing, we need to analyze the sign of the derivative of the function. In this case, the derivative of f(x) is f'(x) = 6x^2 + 6x - 12. We can find the critical points by setting the derivative equal to zero: 6x^2 + 6x - 12 = 0. Solving this equation gives us x = -1 and x = 2.
To determine the intervals of the function, we can create a sign chart:
x-2-1023f'(x)+0-0+
From the sign chart, we can see that the function is increasing on the intervals (-infinity, -1) and (2, infinity), and decreasing on the interval (-1, 2).
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(a) Intervals of Increase:
[tex]\[ (-\infty, -3) \cup (2, \infty) \][/tex]
Interval of Decrease:
[tex]\[ (-3, 2) \][/tex]
(b) Local Minimum and Maximum:
Local Maximum: [tex]\( x = -3 \)[/tex]
Local Minimum: [tex]\( x = 2 \)[/tex]
(c) Inflection Point:
[tex]\[ \left(-\frac{1}{2}, f\left(-\frac{1}{2}\right)\right) \][/tex]
(d) Concavity:
Concave Up: [tex]\( (-\infty, -\frac{1}{2}) \)[/tex]
Concave Down: [tex]\( (-\frac{1}{2}, \infty) \)[/tex]
(a) To find where [tex]\( f(x) \)[/tex] is increasing or decreasing, we need to examine the sign of its derivative, [tex]\( f'(x) \)[/tex].
[tex]\[ f(x) = 2x^3 + 3x^2 - 12x \][/tex]
First, let's find[tex]\( f'(x) \)[/tex]:
[tex]\[ f'(x) = 6x^2 + 6x - 12 \][/tex]
To find where [tex]\( f(x) \)[/tex] is increasing or decreasing, we need to find the critical points where [tex]\( f'(x) = 0 \)[/tex] or is undefined.
Setting [tex]\( f'(x) = 0 \)[/tex]:
[tex]\[ 6x^2 + 6x - 12 = 0 \][/tex]
[tex]\[ x^2 + x - 2 = 0 \][/tex]
This quadratic equation can be factored as:
[tex]\[ (x + 2)(x - 1) = 0 \][/tex]
So, the critical points are [tex]\( x = -3 \)[/tex] and [tex]\( x = 2 \)[/tex].
Now, let's test the intervals between and beyond these critical points:
For [tex]\( x < -3 \)[/tex]:
[tex]\[ f'(-4) = 6(-4)^2 + 6(-4) - 12 = 6(16) - 24 - 12 > 0 \][/tex]
Since [tex]\( f'(-4) > 0 \)[/tex], [tex]\( f(x) \)[/tex] is increasing on[tex]\( (-\infty, -3) \)[/tex].
Between [tex]\( -3 \)[/tex] and [tex]\( 2 \)[/tex] :
[tex]\[ f'(0) = 6(0)^2 + 6(0) - 12 = -12 < 0 \][/tex]
Since [tex]\( f'(0) < 0 \)[/tex], [tex]\( f(x) \)[/tex] is decreasing on [tex]\( (-3, 2) \)[/tex].
For [tex]\( x > 2 \)[/tex]:
[tex]\[ f'(3) = 6(3)^2 + 6(3) - 12 = 6(9) + 18 - 12 > 0 \][/tex]
Since [tex]\( f'(3) > 0 \)[/tex], [tex]\( f(x) \)[/tex] is increasing on [tex]\( (2, \infty) \)[/tex].
So, the interval on which [tex]\( f(x) \)[/tex] is increasing is [tex]\( (-\infty, -3) \cup (2, \infty) \)[/tex] , and the interval on which [tex]\( f(x) \)[/tex] is decreasing is [tex]\( (-3, 2) \)[/tex].
(b) To find the local minimum and maximum values of [tex]\( f(x) \)[/tex] :
we need to examine the critical points and the endpoints of the intervals we found.
Since [tex]\( f(x) \)[/tex] changes from increasing to decreasing at [tex]\( x = -3 \)[/tex], [tex]\( f(x) \)[/tex] has a local maximum at [tex]\( x = -3 \)[/tex] .
And since [tex]\( f(x) \)[/tex] changes from decreasing to increasing at [tex]\( x = 2 \)[/tex], [tex]\( f(x) \)[/tex] has a local minimum at [tex]\( x = 2 \)[/tex] .
(c) To find the inflection point:
we need to examine the concavity of [tex]\( f(x) \)[/tex], which is determined by the sign of the second derivative, [tex]\( f''(x) \)[/tex].
First, let's find [tex]\( f''(x) \)[/tex]:
[tex]\[ f''(x) = 12x + 6 \][/tex]
Setting [tex]\( f''(x) = 0 \)[/tex]:
[tex]\[ 12x + 6 = 0 \][/tex]
[tex]\[ x = -\frac{1}{2} \][/tex]
Since [tex]\( f''(x) \)[/tex] is positive for [tex]\( x < -\frac{1}{2} \)[/tex] and negative for [tex]\( x > -\frac{1}{2} \), \( f(x) \)[/tex] is concave up on [tex]\( (-\infty, -\frac{1}{2}) \)[/tex] and concave down on [tex]\( (-\frac{1}{2}, \infty) \)[/tex].
So, the inflection point is [tex]\( \left(-\frac{1}{2}, f\left(-\frac{1}{2}\right)\right) \)[/tex], and the intervals on which [tex]\( f(x) \)[/tex] is concave up and concave down are [tex]\( (-\infty, -\frac{1}{2}) \)[/tex] and [tex]\( (-\frac{1}{2}, \infty) \)[/tex] respectively.
Hillary starts her own business. She quits her $50,000 a year job, rents an office for $15,000 a year, pays wages and salaries of $50,000 a year, utilities of $4,000 a year, and materials of $20,000. She uses her own car for sales work rather than leasing an equivalent car for $6000 a year. If revenues are $140,000, her accounting profit and economic profit are respectively ______ and _____ .
Answer:
accounting profit =$ 51,000
Economic profit = $ 7000
Step-by-step explanation:
In economic profit we consider opportunity cost opportunity cost is next best alternative for gone.
Economic profit =140,000 - 50,000 - 50,000 - 15,000 - 4000 - 20,000 + 6000
= $ 7000
In accounting profit we do not consider opportunity cost.
hence,
accounting profit = 140,000 - 50,000 - 15,000 - 4000 - 20,000
= $ 51,000
If f(x) = 2x – 1 and g(x) = – 2, find [g ◦ f](x).
Answer:
Step-by-step explanation:
Wherever you see an x in g(x) you are supposed to put f(x).
If g(x) = x
then
g(f(x)) = f(x)
g(x) = f(x)
Since g(x) has no xs, then g(f(x)) = - 2
g(x) = -2 no matter what x is in g(x)
g(2x - 1) = - 2
Answer:
[g ◦ f](x)=-2
Step-by-step explanation:
f(x) = 2x – 1
g(x) = – 2
[g ◦ f](x)
This is a composite function. It means we take f(x) and substitute it in for x in the function g(x)
g(x) = -2
There is no x in the function, so g(x) remains the same
[g ◦ f](x)= -2
Connie, a marketing director, lost her job when her company downsized. This is an example of what type of unemployment?
Answer:
Cyclical unemployment.
Step-by-step explanation: It is not part of the natural unemployment rate.
It's caused by the contraction phase of the business cycle. That's when demand for goods and services generated by the company fall dramatically, forcing businesses to lay off large numbers of workers to cut or reduce costs.
A manufacturer of yoga pants sells them for $28 each. They hired some consultants who determined that the cost of manufacturing x pants was C\left(x\right)=x^2-2x-9 C ( x ) = x 2 − 2 x − 9 . a)Write a function for the revenue (the amount of money the company brings in). b)Write a function for the profit (the revenue – cost). c)Find the number of t-shirts they should make to maximize the profit function. Round your answer to the nearest whole number.
Answer:
a) r(x) = 28x
b) p(x) = -x^2 +30x +9
c) 15
Step-by-step explanation:
a) Let x represent the number of items sold. Each sale results in $28 of revenue, so the revenue function r(x) is ...
r(x) = 28x
__
b) p(x) = r(x) - c(x) = 28x -(x^2 -2x -9)
p(x) = -x^2 +30x +9
__
c) The axis of symmetry of ax^2 +bx +c is -b/(2a). Here, the axis of symmetry of the profit function is ...
x = -30/(2(-1)) = 15
15 is the quantity of sales that maximizes profit.
Sid intended to type a seven-digit number, but the two 3's he meant to type did not appear. What appeared instead was the five-digit number 52115. How many different seven-digit numbers could Sid have meant to type?
Answer:
21 ways
Step-by-step explanation:
number = 7 digit
5 digit no = 52115
to find out
How many different seven-digit numbers
solution
first we need to place the two missing 3s in the number 52115
we consider here two cases
case 1 the two 3's appear separated (like 532135 or 3521135)
case 2 the two 3's appear together (like 5332115 or 5211533)
Case 1 we can see that number type as _5_2_1_1_5_
place 3's placeholders show potential locations
( type a ) for 3's separated we will select 2 of 6 place and place 3 in every location so we do this 6C2 = (15) ways
and (type b): again use same step as _5_2_1_1_5_
here 3s together for criterion and we will select 1 of the 6 place and place both 3s here and there are 6 ways.
so that here will be 15+6=21 ways
If 3 and 3 are separate so 6C2 = 15 ways
If 3 and 3 are together so there = 6 ways
= 15 + 6 = 21 ways
URGENT PLEASE ANSWER THIS MATH QUESTION WILL GIVE 20 points
Answer:
Reflects over the x-axis, then translate (x + 3, y + 1).
Step-by-step explanation:
Your have to flip is over the X-axis to get the short side on the bottom.
Then move is 3 places to the right, so X+3. After which it is move 1 place up, Y+1
Reflects over the x-axis, then translate (x + 3, y + 1).
If we put 5 math, 6 biology, 8 engineering, and 3 physics books on a bookshelf at random, what is the probability that all the math books are together?
Answer: [tex]\dfrac{3}{4389}[/tex]
Step-by-step explanation:
Given : Number of math books = 5
Total number of books = 5+6+8+3=22
Number of books except math = 17
Number of ways to arrange 22 books in bookshelf = [tex]22![/tex]
When all math books are together , then we count whole set as one
Now, the number of objects in bookshelf = 17+1=18
Number of ways to arrange books such that all math books are together = [tex]18!5![/tex]
Now, the probability that all the math books are together :-
[tex]\dfrac{5!18!}{22!}=\dfrac{3}{4389}[/tex]
Hence, the probability that all the math books are together [tex]=\dfrac{3}{4389}[/tex]
In triangle ABC, mA=35, mB=40, and a=9. Which equation should you solve for b?
A. sin35/b=sin40/9
B. sin35/9=sin40/b
C. cos35/9=cos40/b
D.b sqaure=9 square-2(9)bcos40
Answer:
B. sin35/9=sin40/b
Step-by-step explanation:
The law of sines tells you ...
sin(A)/a = sin(B)/b
Filling in the given values, you get ...
sin(35°)/9 = sin(40°)/b
Answer:
B.[tex]\frac{sin 35}{9}=\frac{sin 40 }{b}[/tex]
Step-by-step explanation:
We are given that in a triangle ABC. [tex]m\angle =35^{\circ}[/tex]
[tex]m\angle B=40^{\circ}[/tex]
a=9
We have to find an equation which solve for b
We know that a sine law
[tex]\frac{a}{sine A}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]
Using above formula of sine law
Substituting all given values in the above formula of sine law
Then we get
[tex]\frac{9}{sin 35}=\frac{b}{sin 40}[/tex]
By cross multiply then we get
[tex]sin 40\times 9=sin35 \times b[/tex]
[tex] \frac{sin 40 \times 9}{b}= sin 35[/tex]
Using division property of equality
[tex]\frac{ sin 40}{b}=\frac{sin 35}{9}[/tex]
Using division property of equality
Hence, option B is true option for solving b.
Answer:B.[tex]\frac{sin 35}{9}=\frac{sin 40 }{b}[/tex]
(easy) If ΔEFG ~ ΔLMN with a ratio of 3:1, which of the following is true?
segment EG is congruent to segment LM
segment EF is congruent to segment LM
segment EG over segment LN equals segment FG over segment MN
segment EF over segment LM equals segment EG over segment LM
Answer:
segment EG over segment LN equals segment FG over segment MN
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem
The corresponding sides are
EF and LM
EG and LN
FG and MN
The corresponding angles are
∠E≅∠L
∠F≅∠M
∠G≅∠N
therefore
EF/LM=EG/LN=FG/MN=3/1
Answer:
C: Segment EG over segment LN equals segment FG over MN.
Step-by-step explanation:
We are given that [tex]\triangle EFG \sim\traingle LMN[/tex] with ratio 3:1
We have to find the true statement about two similar triangles in given options
When two triangle are similar
Then ratios of all sides of one triangle to its corresponding all sides of another triangle are equal.
Therefore, Corresponding side of EF is LM
Corresponding side of FG is MN
Corresponding side of EG is LN
Ratio
[tex]\frac{EF}{LM}=\frac{FG}{MN}=\frac{EG}{LN}=\frac{3}{1}[/tex]
Hence, segment FG over segment MN equals to segment EG over segment LN.
Therefore, option C is true.
Answer : C: Segment EG over segment LN equals segment FG over MN.
Help please?
If sin O = -sqrt3 over 2 and n < O < 3 pi over 2, what are the values of cos O and tan O?
Answer:
cos(θ) = -1/2tan(θ) = √3Step-by-step explanation:
You know that ...
cos(θ)² = 1 - sin(θ)²tan(θ) = sin(θ)/cos(θ)cosine is negative in the third quadrant (where π < θ < 3π/2)Using what you know about the relationships of these trig functions, you can find ...
cos(θ)² = 1 - ((-√3)/2)² = 1 - 3/4 = 1/4
cos(θ) = -1/2 . . . . . negative square root of 1/4
__
tan(θ) = sin(θ)/cos(θ) = ((-√3)/2)/(-1/2)
tan(θ) = √3
using exponent laws please answer this
Answer:
see below
Step-by-step explanation:
In addition to the exponent rule ...
(a^b)^c = a^(bc)
it is helpful to know the first few powers of some small integers.
5^3 = 125
9^2 = 81
4^3 = 64
2^6 = 64
__
125^3 = (5^3)^3 = 5^(3·3) = 5^981^7 = (9^2)^7 = 9^(2·7) = 9^14(1/64)^3 = ((1/4)^3)^3 = (1/4)^(3·3) = (1/4)^9(1/64)^3 = ((1/2)^6)^3 = (1/2)^(6·3) = (1/2)^18A nontoxic furniture polish can be made by combining vinegar and olive oil. The amount of oil should be three times the amount of vinegar. How much of each ingredient is needed in order to make 34 oz of furniture polish?
Answer:
V=8.5
Step-by-step explanation:
o=oil. vinegar=v. furniture polish=f
O=3v
34= 3v + v
Using a system of guessing and checking if that number fits equation you can tell that 8 causes the equation to be unequal and also 9. You can learn V must be between 8 and 9 so 8.5 might fit the equation. 8.5=V
Final answer:
To make 34 oz of furniture polish, 8.5 oz of vinegar and 25.5 oz of olive oil are needed, with the olive oil being three times the amount of vinegar.
Explanation:
To create 34 oz of nontoxic furniture polish, where the amount of olive oil should be three times the amount of vinegar, we need to solve a simple algebraic equation. Let's denote the amount of vinegar as v ounces. According to the conditions, the amount of olive oil will then be 3v ounces.
The total amount of furniture polish equals the amount of vinegar plus the amount of olive oil:
v + 3v = 34 oz
This simplifies to:
4v = 34 oz
Dividing both sides by 4 gives us:
v = 8.5 oz
Therefore, the amount of olive oil needed is:
3v = 3 Times 8.5 oz = 25.5 oz
To conclude, we need 8.5 oz of vinegar and 25.5 oz of olive oil to make 34 oz of furniture polish.
An object is launched upward from 62.5 meters above ground level with an initial velocity of 12 meters per second. The gravitational pull of the earth is about 4.9 meters per second squared. How long will the object take to hit the ground? 5) Explain which model would you would choose and why.An object is launched upward from 62.5 meters above ground level with an initial velocity of 12 meters per second. The gravitational pull of the earth is about 4.9 meters per second squared. How long will the object take to hit the ground? 5) Explain which model would you would choose and why.
Answer:
5 seconds
Step-by-step explanation:
This follows the pattern
[tex]h(t)=-4.9t^2+v_{0}t+h_{0}[/tex]
It is parabolic and it is used to model projectile motion. This is the model you would use. Now for the math of it.
The v₀ is the initial velocity and the h₀ is the initial height. The whole thing is negative because it is an upside down parabola. Our initial velocity is 12 and the initial height is 62.5. That means that our particular model is
[tex]h(t)=-4.9t^2+12t+62.5[/tex]
h(t) is the height of the projectile after a certain length of time, t, has gone by. We want to know how long, t, it takes the projectile to hit the ground. When something is laying on the ground, its height is 0. Therefore, in order to find how long it takes for the height to be 0, we replace h(t) with 0 and then factor to find the values of t:
[tex]0=-4.9t^2+12t+62.5[/tex]
If you plug this into the quadratic formula you will get that the values of t are
t = -2.55 and t = 5
We all know that the 2 things in math that will never EVER be negative are time and distance/measures, so we can disregard the negative value of time and say that the length of time it takes for the object to hit the ground from its initial height of 62.5 m is 5 seconds.
Solve each equation by graphing. Round to the nearest tenth.
-2x^2+2=-3x
Answer:
x = -0.5 or x = 2
Step-by-step explanation:
Finding solutions graphically is often easier if the equation can be put in the form f(x) = 0. Here, we can do that by subtracting the right-side expression to give ...
(-2x^2 +2) -(-3x) = 0
This could be put in standard form, but there is no need. A graphing calculator can deal with this directly.
The solutions are x = -0.5 and x = 2.
A manufacturer of golf clubs makes a profit of $50 per set on a model A set and $55 per set on a model B set. Daily production of the Model A clubs is between 20 and 50 sets, inclusive, and that of the model B clubs is between 10 and 30 sets, inclusive. The total daily production is not to exceed 50 sets. How many sets of each model should be manufactured per day to maximize the profit?
Answer:
30 sets of model B20 sets of model AStep-by-step explanation:
To maximize profit, the greatest possible number of the most profitable item should be manufactured. Remaining capacity should be used for the less-profitable item.
Up to 30 of model B, which has the highest profit, can be made each day. The remaining amount (20 sets) of the daily capacity of 50 sets should be used to make model A sets.
If sine theta equals three over four, what are the values of cos θ and tan θ?
cosine theta equals plus or minus square root of seven over four, tangent theta equals plus or minus two times square root of seven over seven
cosine theta equals plus or minus seven over four, tangent theta equals negative three over seven
cosine theta equals plus or minus square root of seven over 4, tangent theta equals plus or minus three over seven
cosine theta equals plus or minus seven over four, tangent theta equals negative one over seven
Answer:
In words, Cosine theta equals plus or minus square root of seven over 4,tangent theta equals plus or minus three over root seven
Step-by-step explanation:
Given that sin ∅ =3/4 It means the ratio of the opposite side to the hypotenuse side is 3:4.
Using the Pythagoras theorem we can calculate the hypotenuse adjacent as follows.
a²+b²=c²
a²=c²-b²
a²=4²-3²
a²=16-9
a²=7
a=√7
Then Cos ∅= opposite/ adjacent
=√7/4
Then Tan ∅ = opposite/adjacent
=3/√7
In words, Cosine theta equals plus or minus square root of seven over 4,tangent theta equals plus or minus three over root seven.
Fill in the blank.
1+8+4+7+3+_+1=24
Answer:
0
Step-by-step explanation:
if you added anything else you would be higher than 24
HELPPPP!!!
Select the correct answer.
Which function is an even function?
Answer:
C.
Step-by-step explanation:
p(x)=sin(x) is an odd function since sin(-x)=-sin(x).
q(x)=cos(x) is an even function since cos(-x)=cos(x).
r(x)=tan(x) is an odd function since tan(-x)=-tan(x).
s(x)=csc(x) is an odd function since csc(-x)=-csc(x).
So the only contender seems to be C.
Let's check. To check we have to plug in (-x) in place of (x) and see if we get the same function back since we are looking for an even function.
[tex]f(x)=\cos(\frac{5\pi}{4}x)[/tex]
Replace (x) with (-x):
[tex]f(-x)=\cos(\frac{5\pi}{4}(-x)[/tex]
[tex]f(-x)=\cos(\frac{-5\pi}{4}x)[/tex]
[tex]f(x)=\cos(\frac{5\pi}{4}x)[/tex] since cosine is even; that is cos(-u)=cos(u) where u in this case is [tex]\frac{5\pi}{4}x[/tex].
So f is even.
C. f(x) = cos(x) The cosine function is an even function. So, the correct answer is C. f(x) = cos(x).
An even function is a function that satisfies the following property:
f(x) = f(-x)
Let's examine the provided functions:
A. f(x) = sin(-31)
This is not an even function because the sine function is an odd function, and negating the angle in a sine function doesn't produce an even function.
B. f(x) = tan(3x)
The tangent function is an odd function, so this function is not even.
C. f(x) = cos(x)
The cosine function is an even function. This is the correct answer.
D. f(x) = csc(-1)
The cosecant function (csc) is the reciprocal of the sine function, and as mentioned earlier, the sine function is an odd function. So, the cosecant function is also odd, and this function is not even.
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Assume that females have pulse rates that are normally distributed with a mean of mu equals 72.0 beats per minute and a standard deviation of sigma equals 12.5 beats per minute. Complete parts (a) through (c) below.
(a) If 1 adult female is randomly selected, find the probability that her pulse rate is between 66 beats per minute and 78 beats per minute.
The probability is?
(b) If 4 adult females are randomly selected, find the probability that they have pulse rates with a mean between 66 beats per minute and 78 beats per minute
The probability is?
(c) Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
Answer:
Step-by-step explanation:
Let X be the pulse rates of females
X is N(72,12.5)
a) P(66<x<78) = P(|Z|<6/12.5)
= P(|Z|<0.48) = 2*.1844=0.3688
b) Each person is independent of the other
Hence P(4*66<4x<4*78) = P(|Z|<24/50) =0.3688^4
c) Because parent distribution is normal
In 1 h the minute hand on a clock moves through a complete circle, and the hour hand moves through 1 12 of a circle. Through how many radians do the minute hand and the hour hand move between 1:00 p.m. and 1:45 p.m. (on the same day)?
Answer:
3/2π and π/480
Step-by-step explanation:
The question given says that the minute hand on a clock moves through complete circle in 1 hour, that is 360° or 2π. It also says that the hour hand moves through 1/12 of a circle, that means 30° or π/6.
To know how many radians do the minute hand and the hour hand move between 1:00 p.m. and 1:45 p.m, it's necessary to calculate how many radians move them per minute.
Between 1:00 p.m. and 1:45 p.m 45 minutes have passed. With that information, the radians can be calculated using multiplication and division.
Minute hand: To know how many radians move the minute hand per minute division wil be used.
Movement in an hour/ minutes in an hour
2π rad/60 min= π/30 rad-min
That means the minute hand move π/30 radians in a minute.
Now, multiplication can be used to calculate how many radians move the minute hand in 1h.
(π/30 rad-min)(45 minutes)= 3/2π rad
The minute hand moves 3/2π radians between 1:00 p.m. and 1:45 p.m.
Hour hand: To know how many radians move the hour hand per minute division wil be used.
Movement in an hour/ minutes in an hour
2π rad/(60 min x 12 hours)= π/360 rad-min
That means the minute hand move π/360 radians in a minute.
Now, multiplication can be used to calculate how many radians move the hour hand in 1h.
(π/360 rad-min)(45 minutes)= π/8 rad
The minute hand moves π/8 radians between 1:00 p.m. and 1:45 p.m.
Between 1:00 p.m. and 1:45 p.m., the minute hand on a clock moves 1.5π radians and the hour hand moves π/8 radians.
Explanation:In clock motion, a full circle or a complete revolution equates to 2π radians. So, in 1 hour the minute hand moving through a complete circle means it moves through 2π radians. Since the time duration considered here is 45 minutes, which is 0.75 of an hour, the minute hand sweeps 2π * 0.75 = 1.5π radians.
Similarly, for the hour hand, a one-twelfth of a circle would be 2π/12 = π/6 radians. As the time frame is again 0.75 hours, the hour hand sweeps a distance of π/6 * 0.75 = π/8 radians.
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Which graph shows the solution set of x^2+4x-12/x>0?
Answer:
D
Step-by-step explanation:
Consider the inequality
[tex]\dfrac{x^2+4x-12}{x}>0[/tex]
First, factor the numerator:
[tex]x^2+4x-12=x^2+6x-2x-12=x(x+6)-2(x+6)=(x+6)(x-2)[/tex]
Now, the inequality is
[tex]\dfrac{(x+6)(x-2)}{x}>0[/tex]
The equivalent inequality is
[tex]x(x+6)(x-2)>0[/tex]
On the number line plot doted points -6, 0 and 2 and put signs +, -, +, - from the right to the left. Intervals with + signs are the solution of the inequality:
[tex]x\in(-6,0)\cup(2,\infty)[/tex]
that is represented by D number line.
Answer:
D
Step-by-step explanation:
Choose the correct answer below. A. The first step in the process of statistics is to collect the data. B. Data are typically collected from a sample because it is too difficult and expensive to collect data from an entire population. C. When the results from a sample are extended to the population, it is called inference. D. If data are not collected properly, the conclusions that are drawn will be meaningless.
Answer: The following statements are correct :
Data are typically collected from a sample because it is too difficult and expensive to collect data from an entire population.
When the results from a sample are extended to the population, it is called inference.
If data are not collected properly, the conclusions that are drawn will be meaningless.
The following statement is false: The first step in the process of statistics is to collect the data.
The first step in the process of statistics is to Plan: develop a statistical inquiry that can be answered with aggregation of data.
your bank balance is 515.50. if you write a check to buy a watch, your balance would be 496.11. how much dose the watch cost ? writ a linear equation on that models the situation
The answer is:
[tex]WatchCost=StartingBalance-EndingBalance\\\\WatchCost=515.50-496.11=19.39[/tex]
The cost of the watch is $19.39.
Why?To solve the problem, we can create a linear equation using the given information about the starting balance and the ending balance.
We know that the starting balance was $515.50, and then, after writing a check to buy the watch, the balance was $496.11, so, writing the function we have:
[tex]WatchCost=StartingBalance-EndingBalance\\\\WatchCost=515.50-496.11=19.39[/tex]
Hence, we have that the cost of the watch is $19.39.
Have a nice day!
8.39+(-2.00)+161
i got 167.39 but it isnt correct
so if yall could help me plsssss
Answer:
8
Step-by-step explanation:
167.39 is right but it can be simplified.
1.61 was replaced by (161/100).
3 more similar replacement(s)
839 2 161
(——— + (0 - —)) +
100 1 100
639 + 161 8
—————————
100 1
Sorry if it looks confusing
$2000 borrowed with 10% interest rate, got additional 1000 on the same rate for the same period of repayment. How much would he have saved if he borrow $3000 for the same rate and period of repayment?
Answer:
nothing
Step-by-step explanation:
Loan payments are linear in the loan amount for a given rate and period, so the payments for loans of $2000 and $1000 sum to the amount of payments for a loan of $3000.
The only possible savings (or cost) might come from rounding to the nearest cent. (In any event, the final payment on each loan should make up for any differences due to rounding.)
Answer:
nothing
Step-by-step explanation:
Loan payments are linear in the loan amount for a given rate and period, so the payments for loans of $2000 and $1000 sum to the amount of payments for a loan of $3000.
The only possible savings (or cost) might come from rounding to the nearest cent. (In any event, the final payment on each loan should make up for any differences due to rounding.)
Which is the angle of elevation from C to B?
Answer:
∠4
Step-by-step explanation:
The angle of elevation is the measure of the angle from the horizontal upwards.
The angle of elevation from C to B is ∠4
Angle of elevation from C to B will be ∠4. Option (1) will be the answer.
Angle of elevation of an object from a point:Angle of elevation of an object from a point on the ground is defined by,
"Angle between the horizontal line and line of site (line joining the observer and the object above the horizontal line)"
Following the definition,
Angle of elevation of an object at B from C will be → ∠4
Therefore, Option (1) will be the answer.
Learn more about angle of elevation here,
https://brainly.com/question/6997568?referrer=searchResults
write 4^0 * 2^2 * 3^3 as a single number
BRAINLIEST!!
Answer:
108Step-by-step explanation:
[tex]4^0=1\\2^2=2\cdot2=4\\3^3=3\cdot3\cdot3=27\\\\4^0\cdot2^2\cdot3^3=1\cdot4\cdot27=108[/tex]
Answer:
108
Step-by-step explanation:
4 to the power of 0 is always 1. multiply to 2 to the power of 2 gives you 4. multiplying 4 to 3 to the power of 3 gives you 108 because 3^3 is 27 but if you multiply that by 4, you get 108
In a certain city the temperature (in °F) t hours after 9 AM was modeled by the function T(t) = 52 + 17 sin πt 12 . Find the average temperature Tave during the period from 9 AM to 9 PM. (Round your answer to the nearest whole number.)
To find the average temperature Tave during the period from 9 AM to 9 PM, we need to find the average value of the temperature function T(t).
Explanation:To find the average temperature Tave during the period from 9 AM to 9 PM, we need to find the average value of the temperature function T(t). The formula for the average value of a function over an interval is given by:
Ave = (1/(b-a)) * ∫[a, b] f(x) dx
In this case, a = 0 (corresponding to 9 AM) and b = 12 (corresponding to 9 PM). Plugging in the temperature function T(t) = 52 + 17 sin(πt/12), we get:
Tave = (1/(12-0)) * ∫[0, 12] (52 + 17 sin(πt/12)) dt
Tave = (1/12) * (52t - 204cos(πt/12))
To find the definite integral ∫[0, 12] (52t - 204cos(πt/12)) dt, we evaluate the antiderivative at the upper and lower limits, and subtract the two values:
Tave = (1/12) * ((52(12) - 204cos(π(12)/12)) - (52(0) - 204cos(π(0)/12)))
Learn more about finding average value of a function here:https://brainly.com/question/36772575
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If five numbers are selected at random from the set {1,2,3,...,20}, what is the probability that their minimum is larger than 5? (A number can be chosen more than once, and the order in which you select the numbers matters)
Answer:
the probability that their minimum is larger than 5 is 0.2373
Step-by-step explanation:
For calculate the probability we need to make a división between the total ways to selected the 5 numbers and the ways to select the five numbers in which every number is larger than 5.
So the number of possibilities to select 5 numbers from 20 is:
20 * 20 * 20 * 20 * 20
First number 2nd number 3rd number 4th number 5th number
Taking into account that a number can be chosen more than once, and the order in which you select the numbers matters, for every position we have 20 options so, there are [tex]20^{5}[/tex] ways to select 5 numbers.
Then the number of possibilities in which their minimum number is larger than 5 is calculate as:
15 * 15 * 15 * 15 * 15
First number 2nd number 3rd number 4th number 5th number
This time for every option we can choose number from 6 to 20, so we have 15 numbers for every option and the total ways that satisfy the condition are [tex]15^{5}[/tex]
So the probability P can be calculate as:
[tex]P=\frac{15^{5} }{20^{5} } \\P=0.2373[/tex]
Then the probability that their minimum is larger than 5 is 0.2373
It's time for another financial calculator problem. A UCF student (who has not taken FIN 2100) decides that he really needs a large screen HD TV for football season. The student goes to a "rent to own" center and agrees to rent a TV for $60 per month (end of month). After 36 months, the student will own the TV. Assuming that the student could buy the same TV today for $1,000, what is the interest rate (APR) of renting the TV?
Answer:
interest rate is 38.68 %
Step-by-step explanation:
Given data
installment = $60
time = 36 months = 36/12 = 3 years
principal = $1000
to find out
interest rate
Solution
we know student pay $60 for 36 months
so he pay total = 60 × 36 = 2160
total amount pay by student = $ 2160
so we can find interest rate by given formula
rate = (1/time)(amount/Principal - 1)
put the value time amount and principal here
rate = (1/3)(2160/1000 - 1)
rate = 0.386667
interest rate is 38.68 %